Theorems · Theorem · general topology

mem_nhdsLT_iff_exists_Ioo_subset

∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [NoMinOrder α] {a : α}
  {s : Set α}, s ∈ nhdsWithin a (Set.Iio a) ↔ ∃ l ∈ Set.Iio a, Set.Ioo l a ⊆ s

A set is a neighborhood of a within (-∞, a) if and only if it contains an interval (l, a) with l < a.

Defined in

Mathlib.Topology.Order.LeftRightNhds

Cited by

4 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderTopologyNoMinOrder